Problem

Given $\angle 1 \cong \angle 7$, which lines, if any, must be parallel based on the given information? Justify your conclusion. $a \| b$, Converse of the Corresponding Angles Theorem $c \| d$, Converse of the Alternate Exterior Angles Theorem $a \| b$, Converse of the Same-Side Interior Angles Theorem not enough information to make a conclusion

Solution

Step 1 :The question is asking which lines must be parallel given that angle 1 is congruent to angle 7. To answer this question, we need to understand the properties of parallel lines and the theorems mentioned in the question.

Step 2 :The Converse of the Corresponding Angles Theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.

Step 3 :The Converse of the Alternate Exterior Angles Theorem states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.

Step 4 :The Converse of the Same-Side Interior Angles Theorem states that if two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel.

Step 5 :However, without a diagram or more information about the position and relationship of these angles and lines, we cannot definitively say which lines are parallel. Therefore, the answer should be 'not enough information to make a conclusion'.

Step 6 :Final Answer: \boxed{\text{Not enough information to make a conclusion}}

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Source: https://solvelyapp.com/problems/0uevPnhfSQ/

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